Why simple recurrent summaries are insufficient

The packed recurrent tensor is rectangular, so its spectral radius is not defined. Even gatewise square-block radii do not control the complete Jacobian.

A contraction bound controls metric separation. For a classical deterministic system with exact noiseless readout, arbitrarily small distinct states can still encode different labels. A claim that classification must approach chance therefore needs an observation-noise, finite-resolution, or robustness condition in addition to state contraction.